Frelkins -- thanks for the references. I am pretty philosophically illiterate and it wouldn't surprise me at all to find out that I'm reinventing stuff that has been around for thousands of years.

I did not mean to imply that supernatural entities are identical in every way to mathematical entities; I'm just using mathematical entities as a club to beat up a certain sort of simple-minded materialism. It turns out that even science geeks talk about immaterial entities all the time. That's interesting.

You are right, this is probably not the place to discuss these idea, but I wanted to drop two more bits if anybody is still reading:

No less a mathematician than Kurt Gรถdel spent part of his later years coming up with formal proofs of the existence of God. I personally am not impressed by this proof, but it shows that working too long with the foundations of mathematics can lead one in strange directions.

Another is this web site, Religious Naturalism, which is a sort of clearinghouse for versions of spirituality and religion that are compatible with science.